If you fail a NIC's check the local police are supposed to be notified - I do not recall how that works but I assume it's just a faxed form. Occasionally people do get arrested after the fact where I live; it sometimes makes papers. Actually I remember one instance they arrested them before they even left the store (assume that was a state-run/pistol check, so the state police just notified the locals).

Where I live it's a misdemeanor to lie on the form, not a very serious crime to begin with (talking state law, no idea about fed law).. local police are very subject to local norms and in order to do anything they would need to look at the notification, actually prove the person lied (which possibly is not true or provable easily), get a warrant, make an arrest - then prosecute a victimless misdemeanor, which is all work for them on top of everything else they are tasked with (like investigating crimes with victims involved)..

Soooo most of the time even when someone has clearly lied on the form, at least where I live, I don't think it goes anywhere.